We analyse numerically an SU(3) Higgs model with complete symmetry breaking and radial degree of freedom on asymmetric, periodic lattices. The character of both the Higgs and deconfining transitions is found to depend on the Higgs self-coupling and on a parameter which may simulate the number of flavours. In particular, an increase in the latter leads to the disappearance of the deconfining transition for small Higgs masses.